@ARTICLE\{IMM2011-05925, author = "A. A. Nielsen", title = "Kernel maximum autocorrelation factor and minimum noise fraction transformations", year = "2011", month = "mar", keywords = "Orthogonal transformations, dual formulation, {Q-}mode analysis, kernel substitution, kernel trick, kernel {MAF,} kernel {MNF}.", pages = "612-624", journal = "{IEEE} Transactions on Image Processing", volume = "20", editor = "", number = "3", publisher = "", note = "Matlab code in zip file, {ENVI}/{IDL} code on Dr. Morton J. Canty's home page", url = "http://www2.compute.dtu.dk/pubdb/pubs/5925-full.html", abstract = "This paper introduces kernel versions of maximum autocorrelation factor (MAF) analysis and minimum noise fraction (MNF) analysis. The kernel versions are based on a dual formulation also termed {Q-}mode analysis in which the data enter into the analysis via inner products in the Gram matrix only. In the kernel version the inner products of the original data are replaced by inner products between nonlinear mappings into higher dimensional feature space. Via kernel substitution also known as the kernel trick these inner products between the mappings are in turn replaced by a kernel function and all quantities needed in the analysis are expressed in terms of this kernel function. This means that we need not know the nonlinear mappings explicitly. Kernel principal component analysis (PCA), kernel {MAF} and kernel {MNF} analyses handle nonlinearities by implicitly transforming data into high (even infinite) dimensional feature space via the kernel function and then performing a linear analysis in that space. Three examples show the very successful application of kernel {MAF}/{MNF} analysis to 1) change detection in {DLR} {3K} camera data recorded 0.7 seconds apart over a busy motorway, 2) change detection in hyperspectral HyMap scanner data covering a small agricultural area, and 3) maize kernel inspection. In the cases shown, the kernel {MAF}/{MNF} transformation performs better than its linear counterpart as well as linear and kernel {PCA}. The leading kernel {MAF}/{MNF} variates seem to possess the ability to adapt to even abruptly varying multi- and hypervariate backgrounds and focus on extreme observations.", isbn_issn = "DOI:10.1109/TIP.2010.2076296" }